127edo

127edo, which divides the octave into 127 parts of 9.45 cents each, is another equal division interesting because of its approximations, defined by the commas it tempers out. In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament. In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the 31st prime edo.

MOS Scales of 127edo